1. Commuting graphs for elements of order three in finite groups
- Author
-
Nawawi, Athirah Binti, Walker, Louise, and Rowley, Peter
- Subjects
512 ,commuting graph ,elements of order three ,symmetric group ,diameter ,connectivity - Abstract
Let G be a finite group and X a subset of G. The commuting graph C(G,X) is the graph whose vertex set is X with two distinct elements of X joined by an edge whenever they commute in the group G. This thesis studies the structure of commuting graphs C(G,X) when G is either a symmetric group Sym(n) or a sporadic group McL, and X a conjugacy class for elements of order three. We describe how this graph can be useful in understanding various aspects of the structure of the group with a particular emphasis on the connectivity of the graph, the properties of the discs around some fixed vertex and the diameter of the graph.
- Published
- 2013